Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk03 E 030001

A kernel-checked arithmetic fact

The declaration e_030001 is a small, self-contained theorem in the framework's machine-checked library of formal theorems. It states that for a particular set of six numerical indices, the value of a function called m2Num equals eight times the value of another function called explicitZ at the same indices. The proof is a direct computation, marked by the word decide, meaning the kernel of the proof system verified the arithmetic by evaluating both sides and confirming they are equal.

This identity is part of a larger verification effort in the framework's gravity analysis, specifically within a file named ReggeExactMidpointM2TTIdentity4D. The name suggests it concerns a midpoint evaluation in a four-dimensional setting, related to an identity involving the letter T. The theorem is one of many similar statements in the same file, each covering a different combination of indices. Together, they form a chunk of a numerical table that the framework is checking for internal consistency.

The theorem does not claim anything about the physical meaning of the numbers. It does not say that m2Num represents a physical quantity, nor that explicitZ does. It does not assert that the identity holds for all possible inputs, only for the specific six indices listed. The proof does not derive the identity from deeper principles; it simply computes both sides and finds them equal. The scope is exactly the one line of the theorem: for these indices, the two expressions agree.

In plain terms, this is a bookkeeping check. The framework is building a large structure of formal proofs, and this declaration is one line in that ledger, confirming that a particular arithmetic relation holds. It is a necessary but minor step, not a standalone result about gravity or about the framework's broader claims. The reader should take it as evidence that the framework's computational checks are being carried out with machine precision, not as a statement about the physical world.

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

What this page does not claim

The theorem does not claim that the identity holds for any indices other than the specific six listed. The theorem does not assign physical meaning to the functions m2Num or explicitZ. The theorem does not derive the identity from any deeper principle; it verifies the arithmetic directly.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/Analysis/ReggeExactMidpointM2TTIdentity4DM2NumChunk03.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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